WOLFRAM|DEMONSTRATIONS PROJECT

Theoretical Model: Condorcet's Jury Theorem, Part 1

​
number of voters
N
odd
even
both
31
probability bias
ϵ
0.01
This is the first of five Demonstrations about Condorcet's jury theorem (1785). It uses the formula
P(N,p)=
N
∑
k=⌈N/2⌉

N
k
×
k
p
1-p
N-k
)
, where the probability
p=0.5+ϵ
and
N
is the number of voters. The theorem states if the voters are independent and each has probability
p=0.5+ϵ>0.5
of voting for the correct choice, then the probability
P(N,p)
of the majority voting for the correct choice is larger than
p
and converges to one as the population
N
goes to infinity.